The present paper is devoted to a systematic study of the combinatorial interpretations of the moments and the linearization coefficients of the orthogonal Sheffer polynomials, i.e., Hermite, Charlier, Laguerre, Meixner and Meixner-Pollaczek polynomials. In particular, we show that Viennot's combinatorial interpretations of the moments can be derived directly from their classical analytical exp...

We investigate generalizations of the Charlier polynomials on the lattice N, on the shifted lattice N + 1 − β, and on the bi-lattice N ∪ (N + 1 − β). We show that the coefficients of the three-term recurrence relation for the orthogonal polynomials are related to solutions of the fifth Painlevé equation PV (which can be transformed to the third Painlevé equation). Initial conditions for differe...

We investigate generalizations of the Charlier and the Meixner polynomials on the lattice N and on the shifted lattice N + 1 − β. We combine both lattices to obtain the bi-lattice N ∪ (N + 1 − β) and show that the orthogonal polynomials on this bi-lattice have recurrence coefficients which satisfy a non-linear system of recurrence equations, which we can identify as a limiting case of an (asymm...

Westerhof N, Elzinga G, Van den Bos GC (1973) Influence of central and peripheral changes on the hydraulic input impedance of the systemic arterial tree. Med Biol Eng 11: 710-723 Wilcken DEL, Charlier AA, Hoffman Jffi, Guz A (1964) Effects of alterations in aortic impedance on the performance of the ventricles. Circ Res 14: 283-293 Winer BJ (1971) Statistical Principles in Experimental Design. ...

A combinatorial construction of the multiple stochastic integral is developed using sequences in Clifford (geometric) algebras. In particular, sequences of Berezin integrals in an ascending chain of geometric algebras converge in mean to the iterated stochastic integral. By embedding such chains within an infinite-dimensional Clifford algebra, an infinitedimensional analogue of the Berezin inte...

We analyze the asymptotic distribution of roots Charlier polynomials with negative parameter depending linearly on index. The cluster curves in complex plane. determine implicit equations for these and deduce limiting density root supported curves. proof is based a determination Cauchy transform specific region careful application saddle point method. obtained result represents solvable example...

This paper concerns with a generalization of Sz?sz-Baskakov operators, which includes Boas-Buck-type polynomials. The convergence properties are studied in weighted space and the rate is obtained by using modulus continuity. A Voronovskaya-type theorem investigated. Also, theoretical results demonstrated choosing particular cases polynomials, namely Appell Hermite Gould-Hopper Laguerre polynomi...

Molecular-dynamics-derived numerical probability density functions (PDFs) have been used to illustrate the effect of different models for thermal motion on the parameters refined in a crystal structure determination. Specifically, anharmonic curved or asymmetric PDFs have been modelled using the traditional harmonic approximation and the anharmonic Gram-Charlier series treatment. The results sh...